Question

How do you factor this..?

Answer 1

\[4x ^{2}-y ^{2}+4y-4\]

Answer 2

unless your missing an x on that last term, I don't see anything more than a difference of squares with the 2 first terms and a simple factorizing of 4 on the last 2.

Answer 3

It's written correctly

Answer 4

ok, so, difference of squares for 4x^2 - y^2. What are the square roots of both terms?

Answer 5

(2x-y)(2x+y)

Answer 6

oh, wait, no, silly me... Ok, you're right for the difference of squares, that's indeed what you should get by doing, but there's something better to do with this equation. Let's just take this :
y^2-4y+4
This is simply a (y+a)^2 type equation

Answer 7

yes.

Answer 8

But what do you do with the -4?

Answer 9

basically, to get to (y+a)^2, you need y^2 to be positive, so we can simply take the minus out of the whole equation :
-(-4x^2+y^2-4y+4)

Answer 10

Oh, I understand! (y-2+2)(y-2-2)

Answer 11

great! That's exactly it!